Re: Two_questions

["Fred E.J. Linton" <fejlinton@usa.net>]

Correction/clarification to previous note: in what follows, the sloppy phrase

> ... the resulting u' is the same as the result of conjugating all the values
of u by the transposition ...

should be replaced by the more accurate expanded version

> ... the h' (as below) resulting from u' is the same as what Sammy gets by
conjugating all the values of the h that arises from u by the transposition
... 

Sorry for the sloppy writing. 

Cheers, -- Fred

------ Original Message ------
Received: Sun, 24 Jun 2012 08:09:45 PM EDT
From: "Fred E.J. Linton" <fejlinton@usa.net>
To: André"  <joyal.andre@uqam.ca>Cc: "categories" <categories@mta.ca>
Subject: categories: Re: Two_questions

> Salut, André,
> 
> I'm ashamed how long it took me to come to this realization, but
> you were absolutely correct in your surmise that, when one lets ...
> 
>> ... E' be the set obtained from E by
>> adding copy p' of p. There are two embeddings u,u':E-->E',
>> the first u is the inclusion of E in E', and the second u' is defined  
>> by putting u'(p)=p' and u'(x)=x for x different than p.
> 
> ... the resulting u' is the same as the result of conjugating all the
values
> of u by the transposition t that exchanges p with p'. Thus, the ...
> 
>> ... pair of homomorphisms h,h':E!-->E'! the equaliser of which
>> is the stabiliser S(p) of p in E!.
> 
> ... that arises is exactly the same as the pair Sammy's argument 
> would adduce, and the only respect in which ...
> 
>> This last argument seems to differ from the argument you have presented.
> 
> is that for Sammy it was enough to observe that h and h' differ SOMEWHERE  
> when E is more than just {p}, while what you observe is rather more, namely,

> that h and h' actually differ EVERYWHERE other than on S(p), i.e., that  the

> ONLY place where h and h' do NOT differ is S(p) :-) .
> 
>> Am I making an error?
> 
> Only in thinking that seeming difference makes any real difference :-) .
> 
> Cheers,  -- Fred



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